Terrestrial dark matter detection experiments probe the velocity-space distribution of dark matter particles in the vicinity of the Earth. We present a novel method, to be used in conjunction with standard cosmological simulations of hierarchical clustering, that allows one to extract a truly local velocity-space distribution in exquisite detail. Preliminary results suggest a new picture for this distribution which is decidedly non-Maxwellian but instead is characterized by randomly positioned peaks in velocity space. We discuss the implications of these results for experiments to detect axions and weakly interacting massive particles.